Pressure Output Feedback Control of Tollmien–Schlichting Waves in Falkner–Skan Boundary Layers

Abstract

This paper investigates the use of point wall pressure measurements for output feedback control of Tollmien–Schlichtingwaves in Falkner–Skan boundary layers.Anewapproach is presented for input–outputmodeling of the linear dynamics of the fluid system and the integration withH2∕Linear Quadratic Gaussian reduced-order control design. The pressure output at the wall is related with the global perturbation velocity field through the linearized pressure Poisson equation. A Kalman filter is subsequently used to obtain time-resolved estimates of the velocity field using pressure information at discrete points at the wall. The estimated field is in turn used to calculate an optimal state feedback control to suppress the instabilities. The controller is designed in a feedforward, a feedback, and a combined feedforward/feedback actuator/sensor configuration. It is shown that combined feedforward/feedback control gives the best tradeoff between robust performance and robust stability in the presence of uncertainties in the Reynolds number and the pressure gradient. Robust performance in off-design conditions is enhanced compared to feedforward control, whereas robust stability is enhanced compared to feedback control.